The invention concerns a method of providing session mobility to an IP based real-time session in a telecommunications network whereby the telecommunications network uses the session initiation protocol for the setup and control of the session. The session comprises a media stream between a first terminal associated to a first network access point of the telecommunications network and a second terminal associated to a second network access point of the telecommunications network. A re-invite session initiation protocol signalling message related to session mobility of said session is intercepted at a session-related session border controller of the telecommunications network. Said session border controller initiates a corresponding session hand-over of said session. In said session hand-over, the media stream of said session is redirected to a new network access point of the first terminal and/or a new terminal.